Poroviscoelastic analysis of borehole and cylinder problems

This paper addresses the phenomena of mechanical creep and deformation in rock formations, coupled with the hydraulic effects of fluid flow. The theory is based on Blot's poroelasticity, generalized to encompass viscoelastic effects through the correspondence principle. Based on the resultant poroviscoelastic theory, stress and deformation analyses are performed. The interactions between the fluid pore pressure diffusion and the elastic/viscoelastic rock matrix deformation are illustrated via two important examples. First, the problem of a borehole subject to a non-hydrostatic stress state, but deforming under plane strain condition, is examined. Second, a cylinder under generalized plane strain conditions is solved. Three rocks, Berea Sandstone, Danian Chalk, and a deep water Gulf of Mexico Shale, covering a wide range of permeabilities, are considered. The significance of poro- and viscoelastic time-dependent effects is discussed.